Find a formula for the inverse of the function f(x)=3x^3 + 2sinx + 4cosx

1 answer:

5 0

Explicit Functiony = f(x) is said to define y explicitly as a function of x because the variable y appears alone on one side of the equation and does not appear at all on the other side. (ex. y = -3x + 5)Implicit FunctionAn equation in which y is not alone on one side. (ex. 3x + y = 5)Implicit DifferentiationGiven a relation of x and y, find dy/dx algebraically.d/dx ln(x)1/xd/dx logb(x) (base b)1/xln(b)d/dx ln(u)1/u × du/dxd/dx logb(u) (base b)1/uln(b) × du/dx(f⁻¹)'(x) = 1/(f'(f⁻¹(x))) iff is a differentiable and one-to-one functiondy/dx = 1/(dx/dy) ify = is a differentiable and one-to-one functiond/dx (b∧x)b∧x × ln(b)d/dx e∧xe∧xd/dx (b∧u)b∧u × ln(b) du/dxd/dx (e∧u)e∧u du/dxDerivatives of inverse trig functionsStrategy for Solving Related Rates Problems1. Assign letters to all quantities that vary with time and any others that seem relevant to the problem. Give a definition for each letter.

2. Identify the rates of change that are known and the rate of change that is to be found. Interpret each rate as a derivative.

3. Find an equation that relates the variables whose rates of change were identified in Step 2. To do this, it will often be helpful to draw an appropriately labeled figure that illustrates the relationship.

4. Differentiate both sides of the equation obtained in Step 3 with respect to time to produce a relationship between the known rates of change and the unknown rate of change.

5. After completing Step 4, substitute all known values for the rates of change and the variables, and then solve for the unknown rate of change.Local Linear Approximation formulaf(x) ≈ f(x₀) + f'(x₀)(x - x₀)
f(x₀ + ∆x) ≈ f(x₀) + f'(x₀)∆x when ∆x = x - x₀Local Linear Approximation from the Differential Point of View∆y ≈ f'(x)dx = dyError Propagation Variablesx₀ is the exact value of the quantity being measured
y₀ = f(x₀) is the exact value of the quantity being computed
x is the measured value of x₀
y = f(x) is the computed value of yL'Hopital's RuleApplying L'Hopital's Rule1. Check that the limit of f(x)/g(x) is an indeterminate form of type 0/0.
2. Differentiate f and g separately.
3. Find the limit of f'(x)/g'(x). If the limit is finite, +∞, or -∞, then it is equal to the limit of f(x)/g(x).

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How do u solve 13 5/9 - 8 1/6?

Alchen [17]

13 5/9 - 8 1/6
= [ (13 * 9) + 5)/9 ] - [ (8*6)+1)/6 ]
= 122/9 - 49/6
= 122*6 - (49*9) / (9*6)
= ( 732 - 441 ) / 54
= 5.389

7 0

3 years ago

Read 2 more answers

How did you get the five consecutive integer that have a product of 524,160

a_sh-v [17]

12*13*14*15*16 = 524160

Idk how to get this answer actually. It's just my first guess, and it happened to be right.

7 0

3 years ago

Suppose that the probability that any particle emitted by a radioactive material will penetrate a certain shield is 0.01. If 10

AnnyKZ [126]

Answer:

a)P=0.42

b) $n\geq 297$

Step-by-step explanation:

We have a binomial distribution, since the result of each experiment admits only two categories (success and failure) and the value of both possibilities is constant in all experiments. The probability of getting k successes in n trials is given by:

$P=\begin{pmatrix}n\\ k\end{pmatrix} p^k(1-p)^{n-k}=\frac{n!}{k!(n!-k!)}p^k(1-p)^{n-k}$

a) we have k=2, n=10 and p=0.01:

$P=\frac{10!}{2!(10!-2!)}0.01^2(1-0.01)^{10-2}\\P=\frac{10!}{2!*8!}0.01^2(0.99)^{8}\\P=45*0.01^2(0.99)^8=0.42$

b) We have, $1-(1-p)^n=P$ , Here P is the probability that at least one particle will penetrate the shield, this probabity has to be equal or greater than 0.95. Therefore, this will be equal to subtract from the total probability, the probability that the particles do not penetrate raised to the total number of particles.